PARIS — There were moments, as recently as last year, when a body that would not stay healthy and on-court results prompted Bethanie Mattek-Sands to wonder whether it was simply time to call it a career after more than a decade as a professional tennis player.

“She was ready to quit,” her husband, Justin Sands, recalled. “She was like, ‘I’m done. I can’t do it. I don’t want to come back.’”

Instead, Mattek-Sands “stuck it out,” in her words, making some significant changes — to her diet after discovering a host of food allergies, to her point-to-point focus. And at age 28, in her 27th Grand Slam tournament, Mattek-Sands earned her most significant victory to date, a 5-7, 6-3, 6-2 upset of 2011 champion Li Na at the rain-soaked French Open on Thursday to join four other American women in the third round.

“I know how I can play, and, you know, there were times when I just physically couldn’t do it,” the 67th-ranked Mattek-Sands said, “and I think that’s really frustrating.”

There was hip surgery less than a week after her wedding in late 2008, a torn shoulder in 2011, a broken right big toe in 2012. Her ranking plummeted from a best of 30th to outside the top 200. She found herself playing in the sport’s minor leagues and going through qualifying just to get into tournaments.

And now?

“She can take more enjoyment out of it, out of playing,” said her coach, Adam Altschuler. “We’ve got to go do it the day after this and the day after that. But it’s great for her to show the world she’s this good.”

By beating the sixth-seeded Li to earn her fourth career win in 25 tries against top-10 players, Mattek-Sands helped give the United States its largest group of women in the third round at the clay-court Grand Slam tournament since six made it in 2004. The five U.S. women left, out of the 15 in the main draw, are the most this far at any Grand Slam tournament since the half-dozen at Wimbledon in 2005.

“We have a lot of talented, young kids,” Mattek-Sands said, then added with a wink and a smile, “Obviously, older kids, too.”

The other Americans in the third round: No. 17 Sloane Stephens and 54th-ranked Jamie Hampton, who also won Thursday, and No. 1 Serena Williams and No. 29 Varvara Lepchenko, who won Wednesday.

“Other than Serena, we’re all a work in progress. A couple years ago, we were not even here. And so we’ve definitely taken a step forward and we’re still progressing and still trying to make that push,” said Hampton, who beat qualifier Anna Karolina Schmiedlova of Slovakia 7-5, 6-2. “Whenever you have a big group like that, there are going to be a few that are going to rise.”

Up next for the 23-year-old Hampton is No. 7 Petra Kvitova, the 2011 Wimbledon champion. The 20-year-old Stephens, meanwhile, faces 92nd-ranked Marina Erakovic, who beat No. 16 Dominika Cibulkova 6-2, 2-6, 6-4 to become the first woman from New Zealand to reach the French Open’s third round.

Stephens, like other players on a wet afternoon, weathered two rain delays during a 6-1, 6-3 win against Vania King of the U.S.

“You literally have nothing to do,” Stephens said. “Should I eat? Do cartwheels?”

Only 18 of 32 scheduled singles matches were completed, with two-time Australian Open champion Victoria Azarenka and 2011 U.S. Open champion Sam Stosur among the winners. Six were suspended in progress — defending champion Maria Sharapova led Canada’s Eugenie Bouchard by a set and a break when they stopped — and eight were postponed entirely, including seven-time French Open title winner Rafael Nadal against Slovakia’s Martin Klizan.

Last year’s runner-up to Nadal, Novak Djokovic, gestured at the dark, threatening sky between points, as if to admonish the clouds for even considering halting play before he could finish a 6-2, 6-0, 6-2 victory over 83rd-ranked Guido Pella of Argentina.

“The most important thing for a player in these interruptions and rain delays is not to get frustrated mentally, because it’s a very fine line. ... Your intensity is there, and suddenly they call it off,” said Djokovic, who is ranked and seeded No. 1 as he bids to complete a career Grand Slam.

“So it’s not easy warming up, cooling off, getting tape, putting off the tape, taking a shower or not taking a shower,” he said. “It’s unpredictable.”

Coming out of a rain delay already down a set but ahead 4-3 in the second, Mattek-Sands reeled off seven consecutive games against Li, the only Chinese player to win a Grand Slam singles title and twice the Australian Open runner-up.

Down 5-0 in the third set, Li made one last stand, taking two games in a row. But Mattek-Sands steeled herself and served out the match on her second attempt, raising both arms overhead after a forehand by Li hit the top of the net and didn’t make it over.

When a reporter wanted to know if she’d been bothered by an illness or injury, Li replied: “Why do you ask me that? Because I lose the match?”

She won both previous meetings against Mattek-Sands, including in straight sets last month on clay at Stuttgart, Germany.

“A little bit surprised ... (on Thursday), the way she’s hitting,” said Li, who has bowed out in the first or second round at half of the eight major tournaments since winning her trophy in Paris.

Mattek-Sands lost before the third round in 24 of her previous 26 Grand Slam appearances, the exceptions being a fourth-round run at Wimbledon in 2008 and a third-round showing at the French Open in 2011.

One difference nowadays is she travels with a list of about two dozen items she avoids eating because of allergies, including gluten and dairy, but also pineapple, peaches, tomatoes and garlic.

There’s also this: After preparing for matches by listening to music (rapper Macklemore of “Thrift Shop” fame is a current favorite), Mattek-Sands focuses from shot to shot and sticks to her tactics better than before.

“Every point is a new point. I have a plan and a purpose each point,” said Mattek-Sands, who now plays 118th-ranked qualifier Paula Ormaechea of Argentina. “I know where I want to hit my serve and where I want to hit my return. I know, basically, my game plan.”

Being able to count on her body helps, too, of course.

“Adam kept believing in her. I believed in her. And we finally found answers with the nutrition side and the rehab side of things. Whatever we’re doing now seems to be working, so we’re going to stick with it,” Justin Sands said. “If she can stay healthy and continue to do what she’s doing, she can beat anybody.”

Mattek-Sands — who was born in Minnesota, lived in Wisconsin (“I’m a Packers fan ’til the day I die,” she says) and now calls Arizona home — has often gained more attention for her fashion choices than her forehand. The metallic gold Wonder Woman ensemble. The argyle cowboy hat. The leopard-print shorts. The eye-black patches.

The knee-high black compression socks she wore Thursday are to help circulation, not start conversation, Mattek-Sands explained.

“I haven’t worn anything too crazy on court for a few years now,” she said, sporting a plain black hoodie at her news conference.

“I feel,” Mattek-Sands added, “like my racket has been doing a lot of the talking.”

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